Anti-terror prosecutors have opened a preliminary investigation, the sources said, adding that no detonators were found in the car.
The car's owner and an associate, both known to police, were arrested on Tuesday, they said.
Paris to open first refugee camp in October
Notre Dame is one of Paris's most visited landmarks attracting 13 million visitors each year.
France has been rocked by a string of deadly attacks claimed by Islamic State group militants.
In July, 86 people were killed when a truck ploughed into a Bastille Day crowd in the southern resort of Nice with Islamic State saying it was driven by one of its followers.
Terror in France: Islamic State owns up to Nice truck attack
Less than two weeks later, two young extremists murdered a priest near the northern city of Rouen.
IS also claimed responsibility for the November 2015 attacks on Paris that killed 130 people and injured hundreds.
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